Power-Efficient ELF Wireless Communications Using Electro-Mechanical Transmitters

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Received November 20, 2019, accepted December 18, 2019, date of publication December 23, 2019, date of current version January 6, 2020.

Digital Object Identifier 10.1109/ACCESS.2019.2961708

JARRED S. GLICKSTEIN 1, (Student Member, IEEE), JIFU LIANG 1, (Member, IEEE), SEUNGDEOG CHOI 2, (Senior Member, IEEE), ARJUNA MADANAYAKE 3, (Senior Member, IEEE), AND SOUMYAJIT MANDAL 1, (Senior Member, IEEE) 1Department of Electrical Engineering and Computer Science, Case Western Reserve University, Cleveland, OH 44106, USA 2Department of Electrical and Computer Engineering, Mississippi State University, Starkville, MS 39762, USA 3Department of Electrical and Computer Engineering, Florida International University, Miami, FL 33174, USA Corresponding author: Jarred S. Glickstein ([email protected])

ABSTRACT Ultra-miniaturized and highly power-efficient ELF (0.3-3 kHz) transmitters are desirable for underground and undersea wireless communications. This paper proposes the use of rotating permanently polarized dipoles (magnets or electrets) for such applications. A power-efficient data modulation scheme based on continuous-frequency FSK (CF-FSK) is also proposed for such electro-mechanical transmitters. Theoretical analysis and simulations show that 7-ary CF-FSK is optimal in the sense that it minimizes average mechanical torque on the mechatronic antenna for a given bit rate. Preliminary experimental results from a prototype ELF magnetic-field based transmitter based on a high-strength rare-earth (NdFeB) magnet and small brushless DC (BLDC) motor are presented. The results highlight local environment challenges such as power line interference that affect the choice of data encoding and modulation schemes. Reliable non-line- of-sight (NLOS) communication through concrete barriers at 100 Hz and ∼0.25 bit/sec is demonstrated at distances up to ∼5 m. The proposed mechatronic antenna and modulation scheme can be scaled up in both frequency and transmit power for more challenging applications in surface-to-undersea, surface-to-cave, and other conductive environments that require ELF channels.

INDEX TERMS Antennas and propagation, communication systems, electromechanical devices, emergency services, magnetic devices, transmitters.

I. INTRODUCTION allows undersea communications to depths of ∼30 m with Wireless communications between the earth’s surface and reasonable transmit power levels [2]. underground or deep-water facilities (mines, shelters, stor- The availability of portable low-power ELF transceivers age areas, tunnels, submarines, undersea cables, etc.) is would immediately enable communications within such very difficult due to the short skin depth δ of electromag- RF-denied environments by enabling bidirectional low-data- netic (EM) waves within conductive media such as earth rate wireless links with the surface. Promising applications or seawater,√ which leads to high attenuation. Fortunately, of such transceivers include oil and gas exploration, search δ ∝ 1/ ω where ω is the frequency. Thus, extremely low and rescue missions (cave rescues including when there frequency (ELF) EM waves can penetrate long distances is significant bodies of water in the signal path under- in RF-denied environments [1]. Note that for convenience, ground), biosensing (e.g., of marine and underground life- here we use ‘‘ELF’’ as shorthand for the combination of forms), underwater and underground Internet of Things (IoT) the ELF, SLF, and ULF ranges (3-30 Hz, 30-300 Hz, and networks (e.g., for ocean pollution monitoring and soil 0.3-3 kHz, respectively), for which EM wavelengths range sensing), inter-submarine and submarine to surface wire- from 105 − 102 km in air. For example, the skin depth in sea less links, underwater autonomous robotics, advanced marine water (conductivity σ ≈ 5 S/m) is δ = 7.1 m at 1 kHz, which biology experiments, geophysics (e.g., subsurface imaging for locating geological conductors, such as ore deposits) The associate editor coordinating the review of this manuscript and [3] and atmospheric science (e.g., studies of the iono- approving it for publication was Cunhua Pan . sphere) [4], [5]. The resulting near-field links have EE and

This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see http://creativecommons.org/licenses/by/4.0/ VOLUME 8, 2020 2455 J. S. Glickstein et al.: Power-Efficient ELF Wireless Communications Using Electro-Mechanical Transmitters

BE fields that propagate independently; here we analyze and those from oscillating electrical currents inside conductors) experimentally demonstrate magneto-inductive (MI) digital are generated by periodic mechanical motion of a magnet or wireless links [6] based only on BE fields, because magnetic electret. This ‘‘all-mechanical transmitter’’ approach is more fields are much less shielded than EE fields by dielectric power-efficient at low frequencies than conventional elec- objects in the medium [7]. trical transmitters, as analyzed in our earlier work [1], [2]. However, near-field ELF links present several problems, It also differs from early electromechanical transmit- including i) limited bandwidth due to the use of low frequen- ters, which simply coupled high-frequency AC generators cies, which in turn limits channel capacity; and ii) the need (e.g., the Alexanderson alternator [20]) to dipole or loop to use electrically small antennas due to device size con- antennas. straints. Fundamentally, the Chu-Harrington limit [8]–[10] Electro-mechanical ELF transmitters have received signif- lower-bounds the quality factor (Q) of small antennas to icant academic attention since the concept was first described ∼ (c/ωa)3, where a is the radius of its enclosing sphere, in 2017 as part of the DARPA AMEBA program [21]. Proto- As a result, the bandwidth and radiation efficiency of small types of transmitters based on rotating magnetic dipoles were dipoles both degrade rapidly with frequency (as ω4a3 and demonstrated in [22], [23]. In both cases, the authors mea- ω3/2a, respectively), while small loops are even worse [2]. sured near-field antenna patterns and dependence of signal Thus, extremely large transmit antennas are necessary for strength versus distance, but did not discuss data transmis- obtaining reasonable bandwidth, channel capacity, and radi- sion. Other work has demonstrated all-mechanical very low ation efficiency at ELF [11]–[13]. ELF receivers can avoid frequency (VLF) transmitters by using piezoelectric elements similar issues by relying on noise matching (rather than to produce oscillating electric fields [24], [25]. The generated impedance matching) to get high sensitivity. In particu- VLF electric fields have either directly been used to transmit lar, broadband noise matching is possible even for high- information [24], or coupled to a magnetostrictive material Q source impedances [14], which allows ELF receivers to generate a magnetic field [25]. These works again pay a with modestly-sized antennas to obtain excellent sensitivity great deal of attention to design of the proposed antenna, but (< 0.1 fT/Hz1/2) over a broad frequency range [15]–[17]. do not consider data transmission. In this paper, we empha- Thus, miniaturized and highly-sensitive ELF receivers are size suitable data modulation and encoding schemes, available, while far-field transmitters remain physically large and also discuss how they influence the design require- and extremely power-hungry. Fortunately, the issue of poor ments for ELF transmitters based on mechanically-rotating radiation efficiency can be avoided in the near-field, where dipoles. the radiated fields are small compared to the stored fields. The paper is organized as follows: Section II presents a In fact, various switching-based direct antenna modula- theoretical analysis of the proposed ELF transmitters. Sys- tion (DAM) schemes have been proposed for decoupling tem design and data modulation are discussed in a theoret- the efficiency, bandwidth, and Q of near-field antennas [18], ical context in Section III, and in an experimental context [19]. Hence this paper focuses on miniaturized near-field ELF in Section IV. A prototype mechanical antenna is used in transmitters, which are the key for realizing short-range (up Section V to examine practical efficacy of the proposed data to ∼1 km) bidirectional wireless links in conductive media. transmission system. Finally, Section VII concludes the paper Since near-field transmitters are not limited by antenna and discusses directions for future work. bandwidth or Q, the key issue for practical implementations is simply field generation efficiency, which is defined as II. THEORETICAL ANALYSIS the magnitude of BE per unit power consumption at a given A. FIELD GENERATION distance r, and has units of T/W. Modern ferromagnetic The proposed ELF transmitters generate oscillating BE fields and ferroelectric materials (permanent magnets and electrets, by physically moving one or more static field sources. respectively) have extremely high energy density and dis- While in principle any type of periodic motion can be used, play strong permanent dipole moments, which makes them in practice mechanical challenges restrict the main choices to promising for achieving high field generation efficiency [1]. oscillations or rotations about a single axis [22]–[25]. Here For example, let us compare a cylindrical NdFeB grade we focus on rotating magnetic or electric dipoles, which N52 magnet (remanent field Br = 1.5 T, length = radius = have the highest possible field generation efficiency [2]. 10 cm) with a N-turn current loop of the same cross-sectional Various motion control methods can be used to imple- area. In order for the two to generate the same static BE field, ment electro-mechanical transmitters of this type. For exam- the loop needs to carry a very large DC current of ∼105/N A. ple, spin transfer torques may be useful for implementing Hence, while the static magnet consumes no power, we esti- highly-miniaturized versions based on rotating nanoscale mate that even a tightly-packed copper loop will consume magnetic dipoles. However, in this paper we limit ourselves > 4 kW. Superconducting coils would eliminate the power to larger devices, for which conventional electric motors are dissipation problem, but modulating their persistent current in the obvious choice. order to transmit data would then become highly challenging. The BE fields generated by rotating magnetic and elec- These facts suggest a fundamentally new approach to ELF tric dipoles have been thoroughly analyzed in our earlier transmitter design in which oscillating BE fields (similar to work [2]. Here we summarize the main results.

2456 VOLUME 8, 2020 J. S. Glickstein et al.: Power-Efficient ELF Wireless Communications Using Electro-Mechanical Transmitters

FIGURE 1. Theoretical near-field B-field patterns created by (a) a rotating magnetic dipole, and (b) a rotating electric dipole. In each case, elevation (El) and azimuth (Az) patterns of |Bx + By + Bz | (the total amplitude measured by a 3-axis B-field sensor) are shown, where θ and φ denote the elevation and azimuth angles, respectively. (c) Qualitative comparison of the power consumed by different sources in order to generate the same B-field intensity at a given distance from an ELF transmitter. Rotating a magnet (near-field), electret (near-field), or electret (far-field) at ω results in a mechanical power consumption P that scales as ω3, ω2, and ω, respectively. On the other hand, using oscillating current in a loop as a / magnetic dipole results in electrical power consumption P that scales as (1 + cω1 2) where c is a constant; here the first term is due to DC resistance and the second due to skin effect.

1) ROTATING MAGNETIC DIPOLE where ax = − cos(θ), ay = 0, az = cos(φ) sin(θ), bx = Consider a permanent magnet of volume V and remanent flux sin(φ) sin(θ), by = − cos(φ) sin(θ), and bz = 0. This function ω/ 2 density Br magnetized along the z-axis. The resulting dipole is the sum of a near-field term ∝ r which dominates −→ = = /µ ∝ ω2/ moment m mbz where m Br V 0. Now assume that when kr 1, and a far-field term r which dominates the magnet is rotated at a rate ω about an axis perpendicular when kr 1. Thus, rotating electric dipoles also behave as to zˆ (such as the x-axis) to generate an oscillating BE field. relatively omnidirectional sources. However, the spatial dis- tribution of total field amplitude |B +B +B | is significantly The−−→ resulting dipole moment is circularly polarized and given x y z = ω + ω different from the rotating magnetic dipole (see Fig. 1(b)). by m(t) m sin( t)by m cos( t)bz, i.e., the sum of two −−−→ √ (µ ω) / π 2 oscillating dipoles [2]. The quasistatic approximation is valid It has a maximum√ of |Bed,rot | = 3 0 Pr V 4 r 2 in the near-field, i.e., at distances r for which ω c/r and (near-field) or 3 µ0ω /c Pr V / (4πr) (far-field). kr 1, where k = w/c is the wavenumber. The field in this region is then given by 3) COMPARISON BETWEEN MAGNETIC AND ELECTRIC DIPOLES −−−−→ µ0 m 3 X B , = [a cos(ωt) + b sin(ωt)] lˆ, (1) dip rot 4π r3 2 l l The near-field generated by a magnetic dipole decreases with l∈{x,y,z} distance as r−3, while that from an electric dipole decreases −2 −1 where ax = cos(φ) sin(2θ), ay = sin(φ) sin(2θ), and az = more slowly (as r and r in the near- and far-field, respec- 1 + θ = φ 2 θ = 2 φ 2 θ − tively). Also the former is frequency-independent, while the 3 cos(2 ), bx sin(2 ) sin ( ), by 2 sin ( ) sin ( ) 2 = θ ϕ latter increases with frequency as ω and ω2, respectively. 3 , bz ay, and and are the elevation and azimuth angles, respectively. Rotating magnetic dipoles behave as relatively Thus, electric dipoles are preferable for longer-range and omnidirectional sources, as shown in Fig. 1(a). All three field higher-frequency applications. components oscillate in phase, so they can be easily summed up by a multi-axis receiver coil to generate the total field 4) EFFECT OF GROUND PLANES E amplitude |Bx + B√y + Bz|, which has a maximum value given The strength of the B field produced at the location of the 3 by Bdip,rot = (3 3 + 1)Br V /(8πr ). receiver by a rotating dipole in air is effectively doubled by the presence of the Earth. At ELF frequencies with wave- 2) ROTATING ELECTRIC DIPOLE lengths beyond millions of meters, the Earth is an effective An electric dipole p0 of volume V can also be rotated about ground plane for communication from any reasonable eleva- an axis perpendicular to itself to generate an oscillating BE tion of the transmitter above mean sea level [23]. Therefore, field; typical values of remanent polarization Pr = p0/V the model developed in eqn. (1) for a dipole in free space for ferroelectric or piezoelectric materials are 20-50 µC/cm2. predicts half the Bdip,rot that is observed in practice as a result = of the ground plane effect. The field due to the time-varying polarization vector bp ω + ω p0[sin( t)by cos( t)bz] is ikr B. POWER CONSUMPTION −−−→ µ0 e B , = p ω(1 − ikr) The peak electrical power input of a mechanical source is ed rot 4π 0 r2 X ˆ τ + τ ω ω ω · [al cos(ωt) + bl sin(ωt)]l, (2) ( f mod ) d Pelec = = τf + J . (3) l∈{x,y,z} ηmηe dt ηmηe

VOLUME 8, 2020 2457 J. S. Glickstein et al.: Power-Efficient ELF Wireless Communications Using Electro-Mechanical Transmitters

Here J is the total moment of inertia of all moving parts (magnet, bearings, and rotor), τf is the torque due to mechanical losses (air friction, bearing loss, etc.), and τmod = J(dω/dt) is the torque due to frequency modulation (used to transmit data). Also ηm and ηe are the efficiency of the motor and the drive electronics, respectively. The components of τf due to air friction and bearing loss scale as ω2 V 2 and ωV , respectively, where V is the volume of the source [26]. Thus the mechanical power consumption ωτf required to generate E ω a target B-field magnitude increases rapidly with , although FIGURE 2. Proposed system design for transmitter producing BE-field the increase is less rapid for rotating electric dipoles that signals from supplied input data. generate stronger BE-fields as ω increases, which allows V to be reduced while keeping |B| constant. Fig. 1(c) summarizes worth noting that we do not consider such distributed trans- this analysis by showing qualitative estimates of the power mitters to be useful as phased arrays. This is because the very required to generate a given BE-field amplitude using rotating long wavelengths at ELF (e.g., 105 m at 3 kHz in air) ensure magnetic and electric dipoles as a function of frequency that even km-scale arrays have sub-wavelength apertures. (assuming the total source volume remains fixed). The power As a result, the fields from individual sources simply add in consumption of a conventional coil-based near-field transmit- phase. ter is also shown for comparison. Clearly, mechanical transmitters are only beneficial up to a certain maximum operating 3) INTERACTIONS BETWEEN ROTATING DIPOLES frequency fmax . Next we discuss design methods to reduce One challenge with using distributed transmitters is the the power consumption of all-mechanical transmitters, thus dipole-dipole coupling between nearby sources, which increasing the value of fmax . increases power consumption by creating an additional coupling torque τc that must be supplied by the motors. For 1) SHAPE OF THE DIPOLE example, in the prototypical case of identical magnets of The shape of the rotating source (magnet or electret) does moment m separated by a distance d = dzˆ and rotat- not affect the dipole field, which only depends on vol- ing synchronously about the x-axis, the coupling torque ume V . Thus, we can reduce power consumption by mini- is mizing J while keeping V fixed to maintain field strength. 2 −→ 3µ0m For example, axially-rotating cylinders of length l have τ =m E × BE = sin(2ωt)xˆ, (4) c π 3 J = ρV 2/(2πl), so J can be reduced by increasing the aspect 8 d / ratio l R of the cylinder while keeping V constant. Moreover, which fluctuates sinusoidally at a frequency 2ω while large aspect ratios also tend to reduce air friction. Thus, decreasing with distance as 1/d3. Coupled electrets with a we focus on diametrically-polarized and axially-rotating dipole moment p behave similarly: the resulting torque is the cylinders with large aspect ratios as field sources. However, 2 2 same as eqn. (4) once µ0m is replaced with p /0. the resulting long and thin shapes are fragile and prone to While the analysis above predicts that τc oscillates at a mechanical instability during high-speed rotation (e.g., due frequency of 2ω in both cases, in practice the fluctuations in to the advent of lateral oscillations) [27], [28]. τc are random since ω is modulated to transmit data [2]. For- tunately, much of the electrical power required to supply such 2) DISTRIBUTED TRANSMITTERS quasi-oscillatory torques can be recovered by using regener- The strong dependence of inertia on physical size (e.g., ative braking methods [29]. Nevertheless, the motor drivers J ∝ R4 for cylinders) suggests that distributed trans- must be appropriately sized to handle the rapidly-fluctuating mitters consisting of an array of small sources should be peak power requirements. more power-efficient than a single large source of the same total volume. For example, consider dividing the source into III. SYSTEM DESIGN N > 1 identical synchronously-rotating elements that are A. DATA MODULATION scaled down as R ∝ N −1/2 to keep the overall volume A block diagram of a single-element electro-mechanical ELF V constant. In this case, J per array element decreases as transmitter is shown in Fig. 2; distributed designs will be V 2/N and torque due to air friction decreases as 1/N 2. The considered in later work. Most of the design complexity generated field per array element decreases as V /N, and thus resides within the digital controller, which i) performs power overall field magnitude remains constant while the net power management functions, ii) generates the modulation wave- consumption Pelec decreases for the system of N elements. form given the input data, and ii) controls the motion of the Thus, the effects of mechanical inertia on the system are field source (assumed to be a cylindrical permanent mag- reduced. Moreover, such distributed transmitters also provide net) through a DC-AC power converter (inverter) and motor built-in redundancy and robustness to localized failures. It is driver.

2458 VOLUME 8, 2020 J. S. Glickstein et al.: Power-Efficient ELF Wireless Communications Using Electro-Mechanical Transmitters

The data modulation scheme, which is shown within the further improvements in compression ratio by using special- dashed box in Fig. 2, is the focus of much concern in the ized compression algorithms that make effective use of the design of power-efficient ELF communications. The pro- proposed reduced character set. Such a scheme is described posed scheme should address the fundamental problem of in Section III-D. power-efficient control of a mechanical device with high inertia and stored energy. We define efficient modulation schemes 2) MODULATION WAVEFORM as those which minimize the additional torque τmod required Energy consumption can be further reduced by packing mul- by the motor to maintain the desired bit rate RB. Given RB, tiple bits within each symbol to decrease the symbol rate we then wish to minimize the symbol rate RS by maxi- RS . In earlier work, we developed a multiple frequency-shift mizing the number of bits within each symbol. Continuous keying (MFSK)-based scheme for this purpose [1]. MFSK phase modulation (CPM) methods such as continuous-phase is a M-ary orthogonal modulation scheme in which M is the frequency shift keying (CP-FSK), Gaussian minimum shift size of the alphabet (number of frequencies) and each symbol / keying (GMSK), and shaped-offset quadrature phase-shift represents log2(M) bits, resulting in RS = RB log2(M). keying (SOQPSK) are promising for this purpose. The result- However, a standard MFSK waveform has discontinuous ing waveforms have i) continuous phase, which results in phase ϕ(t) due to rapid jumps between the symbols, which high spectral efficiency and low out-of-band emissions, and results in large spikes in the instantaneous frequency ω(t) = ii) a constant envelope (CE), which maximizes power effi- dϕ(t)/dt. CP-FSK is a well-known variant of MFSK that ciency [30]. In addition, rotating dipoles naturally generate keeps ϕ(t) continuous, i.e., eliminates frequency spikes by CE waveforms; therefore, CPM is well matched to the phys- generating a CPM waveform [34]. ical constraints of electro-mechanical transmitters. However, A generic M-ary CPM waveform s(t) is defined as the initial phase of each CPM symbol depends on the earlier n X ones (i.e., the symbols have phase memory), which makes s(t) = Ac cos(ω0t + 2π αihiq(t − iT )), (5) the design and implementation of an optimal receiver more i=0 complicated. The optimum receiver operates by detecting where amplitude Ac is a constant proportional to the dipole sequences of symbols, rather than on a bit-by-bit basis [31]. 1 α moment; T = is the symbol period; i are the log2(M)- Fortunately, the necessary methods for detecting sequences, RS bit data symbols; hi is the modulation index (which can vary such as maximum likelihood sequence estimation (MLSE) from symbol to symbol in multi-h schemes); and q(t) is the using the Viterbi algorithm, are well known and can be readily phase response function. CPM schemes can be classified implemented at the low data rates (< 1 kbps) supported by dq = using q(t) or its derivative dt g(t), which is known ELF links. as the frequency response function. For example, LRC and LREC schemes use raised cosine and rectangular frequency B. MINIMIZING POWER CONSUMPTION pulses of length L symbols, respectively. The term CP-FSK Our proposed approach to enable power efficient and refers to LREC schemes with L = 1 that define g(t) to be highly-miniaturized wireless ELF data transmission consists 1/(2T ) for 0 < t < T and zero otherwise. Thus, they are of two steps. The first is source coding to compress the commonly referred to as 1REC, denoting CPM schemes with data by removing redundancy. The second is to minimize the rectangular frequency pulses of length T and phase memory τ ωτ modulation torque mod and associated power mod supplied g(t) communicated across one symbol. CP-FSK waveforms by the motor while maintaining the desired bit rate RB. are continuous, but the symbols are not orthogonal unless h 1 is a multiple of 2 . 1) DATA COMPRESSION In order to understand the properties of CP-FSK, it is useful The total energy required to transmit a given message within to first consider a conventional MFSK waveform s(t), which a specified time can be reduced by compressing the source is defined as data, which in turn reduces the necessary bit rate RB. For ω π1 . example, consider DEFLATE, which is a well-known lossless s(t) = Ac cos( 0t + 2 f × m(t)) (6) data compression algorithm used in PNG images, ZIP files, Here m(t) is the digital data to be transmitted, 1f sets the etc. [32]. DEFLATE is a computationally-efficient scheme frequency steps between symbols, and ω0 is an integer multi- that combines the Lempel-Ziv algorithm (LZ77) [33] with ple of 1f to ensure orthogonality between them. Signals for Huffman coding to compress typical plain text by ≈ 3×. which m(t) ∈ [0, 1] result in binary FSK, where each symbol However, DEFLATE operates on data encoded in ASCII contains a single bit. Similarly, signals for which m(t) ∈ [0, which requires 8 binary bits per character. To further com- M − 1] result in MFSK. press the input message, a reduced character set is imple- By contrast, a M-ary CP-FSK waveform is defined as mented consisting of numbers 0-9, letters A-Z, and a limited Z t set of punctuation (space, comma, period, semicolon, excla- s(t) = Ac cos ω0t + 2π1f m(t1)dt1 , (7) mation mark). Using this reduced set of at most 49 characters, 0 only 6 binary bits are required per character. Nevertheless, where all terms remain as previously defined. Comparing DEFLATEis written to operate on ASCII data; thus we expect eqns. (5) with (6), we see that the instantaneous phase

VOLUME 8, 2020 2459 J. S. Glickstein et al.: Power-Efficient ELF Wireless Communications Using Electro-Mechanical Transmitters

modulation driven by m(t) is replaced with an integral that deﬁnes the phase response function. This integral ensures that ϕ(t) remains continuous (as required for a CPM waveform), but discontinuities remain in its derivative dϕ(t)/dt = ω(t). As a result, large spikes occur in both the angular acceleration α(t) = dω(t)/dt and modulation torque τmod (t) = Jα(t). As described in [1], these can be removed by low-pass ﬁlter- ing the integral before phase modulation, resulting in

s(t) = Ac cos (ω0t + 2π1f × (n ∗ h)(t)) , (8) where h(t) is the impulse response of the low-pass filter (LPF) FIGURE 3. Normalized value of rms angular acceleration versus the ≡ R t number of CF-FSK symbols. and n(t) 0 m(t1)dt1 is the filtered version of m(t). This continuous-frequency FSK (CF-FSK) scheme ensures that both ϕ(t) and ω(t) remain continuous, which in turn ensures that α(t) and τmod remain finite. The choice of h(t) is relatively arbitrary. For example, we can use a boxcar function h(t) = rect(t/TS )/TS of width TS = 1/RS , which cor- responds to a sinc function in the frequency domain. This particular filter is interesting because it keeps ω(t) piecewise linear, which in turn simplifies motor design by restricting τmod (t) to a finite set of values. The value of α(t) decreases along with 1f . However, reducing 1f eventually destroys orthogonality between the symbols, which increases the bit error rate (BER). Assuming coherent or noncoherent detection, the minimum step size FIGURE 4. Simulated instantaneous frequency offset (top) and that ensures orthogonality is known to be 1f = RS /2 or RS , modulation rate (bottom) for CP-FSK and CF-FSK, both with M = 8. respectively, for CP-FSK. For simplicity, we assume the same limit for CF-FSK. σ Assuming constant 1f , increasing the number of symbols exact calculation of D as well as the approximation is shown M = × M also increases the torque required to transmit a message. in Fig. 3. The optimal value is 7, which results in a 2 σα M = Increasing the number of symbols increases the maximum reduction in compared to binary modulation ( 2). and rms values of m(t), thereby increasing the required rms motor acceleration (and therefore power) to transmit a sym- C. SIMULATION RESULTS Simulated CP-FSK and CF-FSK waveforms generated by the bol. However, each symbol represents log2(M) bits and so increasing the number of levels increases the number of bits same random data stream are shown in Fig. 4. CF-FSK limits σ . × π 2 per symbol, thus decreasing the number of symbols required α to 0 152 2 RB, which is within 15% of the theoretical to transmit the same message. This trade-off results in an result. Fig. 5 compares the power spectra of the two schemes optimum value of M that minimizes the power required to estimated using Welch’s method [35]. The figure shows transmit a fixed-length message. that the transmitted bandwidth BS is slightly smaller for The rms value of α(t) over the message duration, which CF-FSK than CP-FSK. The bandwidth for both schemes sets the peak motor power rating, is represented by σα. can be approximately derived by using Carson’s rule for 1 Assuming the transmitted data is random, the rms angular frequency modulation [36], which states that for (f ) f0, ≈ 1 + frequency step is σ1ω = 2π × 1f × σD, where σD is the BS (M f 2fm), where fm is the bandwidth of the input / 1 rms value of the transmitted data values D. Since the symbol signal. In our case fm ≈ RS 2 = f ; we therefore expect that ≈ + 1 = 1 = duration 1t ≡ 1/Rs = 2/1f for coherent detection and BS (M 2) f 10 f for M 8, which agrees with the α(t) = dω(t)/dt = 1ω/1t, σα is given by simulation results shown in Fig. 5. 2 σα = πR σ . s D (9) D. DIFFERENTIAL CODING σ Each symbol represents log2 M bits, so α in terms of the bit The proposed M-ary CPM scheme can be combined with dif- rate RB is given by ferential coding to provide several benefits over conventional α π 2 σ FSK. Each symbol i in such an M-ary scheme has a value in RB D σα = . the range αi ∈ [0, M − 1] for M unique data symbol values. 2 (10) (log2(M)) To increase the number of bits transmitted per symbol, differ- If we assume that each symbol√ is equally probable, σD can ential encoding is applied in a manner similar to differential be approximated as M/ 12 for M 1. The normalized phase shift keying (DPSK). In a differential scheme, data σ / π 2 acceleration α (2 RB) as a function of M predicted by an is transmitted as the change from interval to interval rather

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instantaneous compared with the slow continuously-time- varying frequency of each actual transition. A differential detector is readily adaptable to such a signal. The differential detection scheme introduces some memory to the signal as each received bit depends on both the present and previous received values (m(ti) and m(ti), respectively). As a consequence, one error in transmission produces two received bit errors, which doubles the BER [30]. The proposed CP-FSK scheme avoids increases in BER due to differential coding, as the differential detector uses the tra- jectory of the received signal rather than discrete present and previous values to determine the value of each bit. The phase FIGURE 5. Simulated power spectra of the transmitted waveforms for memory introduced by the modulation scheme may then be = CP-FSK and CF-FSK, both with M 8. used as additional information to increase the confidence of the detector in selecting the most probable current symbol. than as the intervals themselves [30]. For example, DPSK is a binary scheme in which the symbols are encoded by the E. BIT ERROR RATE (BER) ANALYSIS transformation The BER analysis of CPM schemes is relatively complex. For the simplest case of an additive white Gaussian αi = |m(ti) − m(ti−1)| (11) noise (AWGN) channel, the error probability of a maximum A message transmitted with M-ary FSK requires a likelihood (ML) receiver for the i-th transmitted symbol si(t) bandwidth 1f (M − 1) in the receiver as there are M is bounded by fixed-frequency levels which must be observed by the X p Pbe(i) ≤ Q di,k Eb/N0 , (12) receiver. However, consider the case of CPM for the same k6=i value of M. Differential modulation schemes require the use where d , is the Euclidean distance between s (t) and the of a special differential detector. For the case of DPSK, note i k i erroneous detected symbol s (t); E = A2T /(2 log (M)) and the differential detector discards the sign of the difference k b c 2 N are the energy per bit and noise power spectral density, between present and previous transmitted bits and records 0 √ respectively; and Q(x) = 1 [1 − erf(x/ 2)] where erf(x) is only the magnitude. For the proposed CP-FSK modulation 2 the error function [30]. scheme, using a differential detector sensitive to the mag- The worst-case BER (i.e., upper bound) shown in eqn. (12) nitude as well as the sign of each transition, each symbol occurs when all M − 1 symbol errors are equally likely. may take a value in the range [− M−1 , M−1 ]. As a result, 2 2 Finding the upper bound is analytically difficult; instead, here the required bandwidth for the transmission of M unique data we consider the lower bound. The latter can be derived by symbols is only 1 1f (M − 1). Thus, the required bandwidth 2 assuming that, though there are M − 1 possible ways to make for M unique symbols transmitted using M-ary CP-FSK (or an error per symbol, the receiver only makes the most likely CF-FSK) is half that of conventional FSK. errors, i.e., always selects the symbol that is ‘‘closest’’ to the This type of differential coding is impractical to implement transmitted one [31]. Experimental results confirm that this is in conventional FSK as sign-sensitive differential detection a good approximation for the prototype ELF receiver. In this of non-random data will inevitably require the transmission case the minimum possible value of d , (denoted as d ) of long sequences of positive or negative values. In either i k min sets the error performance of the receiver, and the total BER case, no more data of the same sign may be transmitted once is approximately the magnitude |m(ti−1)| = M − 1. The situation could be p corrected by constructing a differential detector sensitive to Pbe ≈ Q dmin Eb/N0 . (13) transitions m(ti)−m(ti− ) rather than m(ti)−m(ti−1) and adding 2 additional frequency shifts within the transmit signal to code The value of dmin for the proposed CP-FSK modulation transitions which accumulate too great a net frequency shift scheme is tabulated for some common values of M in [30, over time. This frequency shift would be indistinguishable p. 66]. In particular, results are tabulated for M = 4 (quater- from a data transition in conventional CF-FSK modulation nary) and M = 8 (octal) for various values of the modulation schemes, only it would occur some time within a symbol index h. The BER for the optimum case (M = 7) is expected period. It is then critical that the differential detector is sensi- to be bounded by these two cases; taking h = 1, in the 2 ≈ . 2 ≈ tive only to transitions at the data clock edge and not within worst case we expect dmin 5 5 for octal and dmin 4 the symbol period, otherwise frequency discontinuities intro- for quaternary 1REC modulation. The resulting BER curves duced to transmit successive differential-coded transitions versus Eb/N0 are shown in Fig. 6. of the same sign would be falsely detected as individual In practice, an AWGN model is not accurate for atmo- bits. In the proposed CF-FSK modulation scheme of Fig. 4, spheric, underground, and undersea ELF and VLF chan- differential coding correction frequency shifts could be near nels [15], [37]. Atmospheric noise at such low frequencies

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FIGURE 6. Theoretical BER performance of a CP-FSK receiver in an AWGN channel. FIGURE 7. Estimated compression ratio performance of DEFLATE, BWT+RLE, and BWT+RLE+RCS algorithms on typical English text (five exhibits impulse-like "sferics" induced by lightning strokes well-known novels) as a function of string length. from storms, and "chorus" or "hiss" emissions from the mag- netosphere, respectively; additional noise sources include power line harmonics and ionospheric resonances. Many of these sources have time-varying and non-Gaussian probability distributions; they are also often correlated with ﬂuctu- ations in the received signal amplitude (i.e., fading events). In addition to noise, underground and undersea propagation is frequency-dependent due to the dispersive medium. Thus, ELF channels exhibit both time- and frequency-dependent fading. The study of BER for CP-FSK or CF-FSK waveforms in such complex channels is left for future work.

F. DATA ENCODING Fig. 3 shows that while M = 7 is the optimum number of FIGURE 8. A labeled photo of the prototype mechanical transmitter. CF-FSK symbols to minimize the torque due to modulation, Controller electronics are not shown in the photo. the curve is nearly ﬂat over the range [4, 15]. Moreover, the maximum frequency excursion for a given symbol rate is The DEFLATE algorithm has not yet been implemented proportional to M. Regardless, we chose to use the optimum for such a reduced character set, so an alternative compression value M = 7. Assuming a differential detector, data with val- algorithm is proposed which operates on any character set. ues in the range [−3, 3] may thus be coded for transmission. A combination of the Burrows-Wheeler transform (BWT) This range is linearly mapped to [0, 6] for convenience. The and run-length encoding (RLE) is used to achieve comparable DEFLATE algorithm operates on messages encoded using compression ratios to DEFLATE in a direct comparison on the ASCII character set and requires one 8-binary-bit byte ASCII data shown in Fig. 7. The Burrows-Wheeler transform per character. Transmission of this data using the 7 available applies block-sorting to rearrange the input message in a way symbols would require 3-septenary-bit bytes to represent all which increases the frequency of runs of identical characters. 256 characters in the ASCII set. However, proposed applica- Then, run-length based compression is applied by replacing tions for ELF transmitters do not necessarily require the entire runs of identical characters in a string with one character ASCII character set to be available. By implementing coding followed by a counter to indicate how many times the bit is of messages using a reduced character set (RCS) as described repeated. For example, a sequence such as "ABBBBC" may in Section III-A, the effective data rate may be increased be replaced by ‘‘AB(3x)C’’. A single byte counter code is by reducing the number of symbols used to represent each used to represent the counter "(3x)" to minimize the num- character. ber of bytes in the transmission-ready signal. Simulation Consider a case where symbols are grouped into two-bit shows this algorithm alone achieves a slightly lower com- bytes. The numbers 00 to 55 in base-6 correspond to the num- pression ratio than DEFLATE. However, implementing a bers 0-9 followed by the Latin letters A-Z in base-36. This reduced character set after BWT+RLE compression results observation offers a convenient way to encode real data while in an effective compression ratio above the performance of leaving 14 additional values (when either MSB or LSB is 6 in DEFLATE. a byte) for punctuation, data compression, and error-checking codes. In this character encoding scheme, each character uses IV. EXPERIMENTAL SETUP two bytes, resulting in an effective data rate that is increased An electro-mechanical transmitter designed to operate at by a factor of 1.5× compared to transmission using the ASCII ∼100 Hz was realized using a small brushless DC (BLDC) character set. motor which drives a magnet made of grade N42 neodymium

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FIGURE 9. Block diagram of the transmitter side of the experiment. FIGURE 10. Block diagram of the receiver side of the experiment. alloy (NdFeB) mounted to a shaft. The transmitter assembly is shown in Fig. 8. The motor is rated for a no-load speed of 10,000 rpm at 12 VDC, weighs 63 g, and is 34 × 33 mm (L × W ) in size with an output shaft 7.1 × 2 mm (L × D). The magnet is a diametrically polarized ring with dimensions 19.05 mm outside diameter, 6.35 mm inside diameter, and 19.05 mm length. Given Br = 1.31 T, the estimated magnetic moment is m = 5.03 Am2. The complete assembly is 38 × 38 × 83 mm (H × W × D) in size. We now discuss design and control of the transmitter as well as an experimental setup for a receiver to test non- line-of-sight (NLOS) ELF communications. Following tests of transmitter capabilities, experimental data transmission results are shown and data encoding/decoding methods are developed to meet environmental restrictions on the wireless channel.

A. TRANSMITTER DESIGN The motor for the transmitter is driven by a power amplifier (PA) (AE Techron 7224) in voltage-output mode with open-loop control signals provided by a programmable voltage source (Keithley 2450 source-measure unit [SMU]) as shown in Fig. 9. Initially, the voltage-frequency characteristic of the motor was experimentally determined. This calibrated FIGURE 11. Measured data at the input to the lock-in amplifier on the relationship was then used to calculate the SMU input wave- receive side at a location 4.67 m away from transmitter, shown (a) before, form necessary for encoding user-specified data using the and (b) after the use of notch filters. CP-FSK and CF-FSK modulation schemes described in the previous section. Finally, the SMU was controlled from a levels for a data bandwidth of 88-116 Hz; the sensitivity of computer over a GPIB bus in order to run an experiment. With the MC95 sensor is effectively constant at 1 mV/mG over this a suitably high 1f between input levels (such as the 4 Hz used range. Initially the receive-side signal path simply consisted in the experiments which follow), errors from this open-loop of a low-noise amplifier (LNA) (SR560, Stanford Research control approach may conveniently be neglected. At low data Systems) with programmable gain connected to an oscillo- rates (such as the 0.25-0.5 bits/sec used experimentally), scope. However, the LNA did not have a sharp enough cut-off GPIB communication latency may be neglected as well. to filter power-line interference without removing the signal itself, so two active twin-T notch filters (tuned to 60 and B. RECEIVER DESIGN 120 Hz, respectively) were added to attenuate these sources. A block diagram of the receiver-side signal path is shown However, while transmitting across a distance greater than in Fig. 10. The receiver uses an inductive single-axis BE-field several meters, the LNA was found to quickly saturate before sensor (Magcheck-95 [MC95] from Magnetic Sciences), with enough gain could be attained. To achieve longer transmis- a rated −3 dB magnitude bandwidth of 25 Hz to 3 kHz. sion distances, a lock-in amplifier (SR860, Stanford Research Interference from power lines poses a challenge to ELF Systems) with extremely high sensitivity (up to 1 nv full-scale communications; in the United States, such interference has input range) was added after the notch filters. The LNA was a fundamental frequency of 60 Hz. The initial goal was to then used as a low-gain preamplifier to set the input-referred transmit the signal between the strong 60 Hz and 120 Hz noise floor and buffer the input to the notch filters. interference lines. Thus, the initial transmit signals used in Fig. 11 shows the spectrogram of a typical 10-bit CP-FSK testing had M = 15 symbols and 1f = 4 Hz between sequence received with and without the use of notch filtering.

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FIGURE 13. Measured dependence of field strength versus distance at 100 Hz.

FIGURE 12. Measured data at the output of lock-in amplifier on the receive side at a location 4.67 m away from transmitter, shown (a) before, and (b) after the use of notch filters. FIGURE 14. Graphic depicting the location of the prototype mechanical ELF transmitter and inductive receiver in an office building. This setup The most invasive noise is the second harmonic at 120 Hz, was used for data transmission in the following sub-sections. which is too close to the signal transmission bandwidth to be filtered out by the lock in amplifier. In Fig. 11(a) (without notch filtering), the LNA is set to a gain of 200, which was The receiver pickup coil has a sensitivity of 1 mV/mG (i.e., the highest achievable before 60 Hz noise saturated the input 104 V/T) over the transmission operating bandwidth, while to the lock-in amplifier. the SR560 pre-amplifier has a noise floor of 4 nV/Hz1/2. With the use of notch filters (see Fig. 11(b)), LNA gain These values correspond to a measurement sensitivity could be increased to 500 before the input to the lock-in of 400 fT/Hz1/2, which is adequate for these tests. However, amplifier saturates, now by the third power line harmonic ∼103 times better sensitivity is possible using state of the art (180 Hz). The built-in filtering provided by the lock-in ampli- BE-field receivers in this frequency range, such as the AWE- fier can reject this term, as shown in Fig. 12: The figure con- SOME instrument [17]. Given that B ∝ 1/d3, using such firms that the third harmonic present at the lock-in output is a sensitive receiver would immediately increase the useful significantly reduced (even for higher LNA gain) compared range of our transmitter by a factor of ∼10. with Fig. 11. However, 180 Hz is still too close to the transmit signal bandwidth to be completely filtered out without also B. WIRELESS NLOS DATA TRANSMISSION attenuating the transmitted signal. Thus, further improve- In order to transmit data, various CP-FSK and CF-FSK wave- ments in receiver sensitivity are possible by using additional forms were generated in the manner described in Section III- notch filters tuned to power line harmonics at 180 Hz, 240 Hz, A. Using the experimentally determined frequency-voltage etc. characteristic of the transmitter motor, transmit signals, such as those shown in Fig. 4, are converted to vectors of V. EXPERIMENTAL RESULTS motor voltage corresponding to the desired transmit fre- A. FIELD STRENGTH VERSUS DISTANCE quency. At low operating frequencies (typical center fre- In initial tests, the field strength versus distance d was quency of 100 Hz with 1f = 4 Hz) and data rates (typical measured at several points from 0.14 to 1.4 meters away symbol period of 2-4 sec), this rudimentary open loop control from the transmitter. The motor speed was kept constant at system is sufficient to demonstrate successful transmission of 100 Hz (6,000 rpm) during these tests. The results, which data. are plotted in Fig. 13, confirm the expected field dropoff Wireless NLOS communications using the mechanical profile. In particular, the measured data is well fit by a transmitter was demonstrated by placing the receiver in a function ∝ 1 . d3 hallway one floor above the transmitter (see Fig. 14). The

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FIGURE 17. Measured peak PSD plotted to demonstrate how each symbol is windowed to recover the transmitted data. FIGURE 15. Computer-generated transmit data bit stream compared with data received from the prototype transmitter. Shown as a red trace in the figure is the peak of the PSD within each 0.5 s window, which is extracted to recover the transmitted signal. The peak PSD shown in Fig. 16 is shown in Fig. 17, with data points plotted on top of the smooth curve for clarity. The 10-symbol transmit sequence has a symbol period of 4 s, resulting in 8 sample points per bit for STFT windows of duration 0.5 s. These data points are split into bit periods as shown by light blue traces in the figure. A piecewise linear fit is used to extract the bit value in each region. Note that the data shown has a dynamic range of −3 Hz to +6 Hz, while the transmitted waveform had a bandwidth −4 Hz to +8 Hz. This error is due to open loop motor control, and can FIGURE 16. Received power spectral density (PSD) of the signal versus time (multicolored, background) with peak intensity (red line, be easily corrected by re-scaling this data before applying a foreground) used to recover the data. linear fit since the received data still satisfies the condition 1f ≥ R = 1 for noncoherent detection, i.e., consists of an S TS receiver was installed on a mobile cart in order to observe orthogonal set of symbols. the ambient noise at various locations in the hallway. At the default location, the distance between transmitter and receiver C. PRACTICAL MESSAGE TRANSMISSION in this setup was approximately 4.67 m with the two separated Practical transmission of data through the link has been by a wall and floor/ceiling. During the tests, transmit data demonstrated using a 233-character excerpt from Shake- bandwidth was reduced to 96-108 Hz by using M = 7 sym- speare’s Hamlet, Act II, Scene 2: bols and 1f = 4 Hz. This narrow bandwidth permits more WHAT A PIECE OF WORK IS MAN! selective (larger Q factor) bandpass filtering in the lock-in HOW NOBLE IN REASON, amplifier to reject ambient noise and power line harmonics, HOW INFINITE IN FACULTY. as described in Section IV-B. IN FORM AND MOVING, Fig. 15 shows i) example transmit data used to generate HOW EXPRESS AND ADMIRABLE. a 10-symbol CP-FSK message (≈28 binary bits), and ii) the IN ACTION, HOW LIKE AN ANGEL. reconstructed receive signal. The raw receive data values are IN APPREHENSION, HOW LIKE A GOD. plotted as a dashed line with the recovered bits shown as a THE BEAUTY OF THE WORLD, solid line at the nearest valid bit value. The figure confirms THE PARAGON OF ANIMALS. successful data transmission. The process of data recovery is now described. For The full data encoding scheme shown in Fig. 18 was convenience, we implemented a simple spectrogram-based developed from the data modulation theory of Section III- decoder rather than the optimal MLSE-based decoder. Data A and preliminary experimental results. It was applied to was captured in the time domain and then post-processed the input data to produce a suitable transmission-ready sig- using a short-time Fourier transform (STFT). Time windows nal. Compression reduced the sequence of 233 characters to of 1 s overlapping by 0.5 s result in an effective frequency 208 characters, 89% of the original size. For demonstration resolution of 1 Hz and a time resolution of 0.5 s, and purposes, parity was not implemented and is left for future generate spectrograms as shown in Fig. 16. Unlike the simu- work. lated sequences, the transmitted signal also includes ramp-up The sequence of 208 characters was represented by and ramp-down features which reduce wear on the motor 416 symbols using the established data encoding system. and function as transmission ‘‘start’’ and ‘‘stop’’ indicators. With a symbol period of 4 seconds, this data is transmitted

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FIGURE 18. Data encoding scheme used with prototype transmitter taking input data as a string of characters to produce a transmission-ready signal with compression and error-checking.

FIGURE 20. Data decoding scheme used to recover the message from received data.

FIGURE 19. Spectrogram of the received signal showing slow drift in transmission frequency over time.

FIGURE 21. Sample section of received CP-FSK signal with critical in 1664 seconds (about 28 minutes). The spectrogram of data features and one error shown as an example. from the entire experiment in Fig. 19 shows an interesting consequence of open-loop voltage control. In a long transmission the transmitter bandwidth shifts, presumably as the motor heats up and coil impedance changes. Using a current source or switching to closed loop control in future work is proposed to correct this problem. Received data is processed using a demodulation scheme to recover the received message from the quadrature receive signal input to the block diagram of Fig. 20. The peak short time PSD of the entire received message is shown in Fig. 19 above. Windowing is applied to the peak PSD to identify the start and length of each symbol using the known symbol period and maximum rate of change in frequency. The piecewise linear fit produces a goodness of fit metric (R2) FIGURE 22. Sample sequence of bits from message transmission which is used to determine whether the symbol window is experiment showing comparison between transmit and receive signals. reasonable. Limited time resolution and errors present at transitions between symbols result in bit windows being less than the windowed bit would not correct this data as this bit has a theoretical 9 samples which would represent a range of 4 sec- smooth profile and the linear fit computed goodness of fit is onds at 0.5 second intervals. In the absence of a clock signal, 0.9932. Implementing parity would allow for this error to be critical features such as peaks and discontinuities are used detected but not corrected. In either case, re-transmission of to identify the start position and length of each bit. These some data is required. features are highlighted in Fig. 21, a sample 10 symbol A short sequence of 10 symbols in the decoded receive sequence from the received message. This sequence also signal is shown in Fig. 22. This sequence is chosen to corre- contains an error at index 378. The receive data decoding spond to the sequence shown in Fig. 21. In the transmission scheme of Fig. 20 shows two methods proposed to detect of 416 symbols, the error shown is the only erroneous symbol such an error. Using goodness of fit to detect an improperly in the sequence. With retransmission of the short sequence

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TABLE 1. Comparison of energy consumption for 100-symbol transmit sequences using FSK, CP-FSK, and CF-FSK modulation schemes.

FIGURE 23. Projected BER performance over distance based on / experimentally determined Eb N0 in two cases: i) using the current B-field sensor, and ii) using the much larger AWESOME B-field −3 receiver. The horizontal line denotes Pbe = 10 . including the erroneous symbol, successful transmission of the message is completed.

D. BIT ERROR RATE (BER) ANALYSIS OF THE PROTOTYPE Using the data collected in the previous section with the receiver placed 4.67 m away from the prototype transmitter, Eb/N0 for the channel is measured to be 13.67 dB, which cor- −22 responds to a negligible BER of Pbe = 2.5 × 10 . In prac- FIGURE 24. Simulated power consumption (at 100 Hz) of an inductive tice, a single symbol error was observed out of 416 symbols coil with the same outer dimensions and magnetic moment as the mechanical ELF transmitter. Plots are shown for various values of fill in the received message, which is promising but insufficient factor ρ, where 1 − ρ is the ratio of inner to outer diameter for the coil. for estimating BER. 3 As magnetic field strength drops off as Bdip ∝ 1/r 2 / and Eb = (As Ts) log2(M) in a non-conductive medium, between the schemes is observed in this data. This is because 6 the bit energy Eb ∝ 1/r . This relationship is used to the non-optimized mechanical design of our prototype results predict BER performance versus distance within such media in the load torque being much larger than the modulation by using the prototype mechanical transmitter. The field torque (i.e., ensures that τL τmod ). strength observed over distance in air (see Fig. 13) is con- From the data in Table 1, average power consumption of sistent with simulations for a magnetic dipole. The expected the prototype mechanical transmitter is 11.0 W during oper- BER performance of the prototype is extrapolated using this ation. We compare this with the power required to generate trend. an equivalent dipole field (with identical 1/r3 drop-off versus We define the theoretical maximum transmit distance as distance) using an electrical coil with the same dimensions as − the distance where Pbe reaches a value of 10 3. This is the prototype transmitter. In Fig. 24, we simulate the power generally considered to be a reasonable upper limit for mes- required to generate an equivalent field with an electrical sage transmission without additional error correction. For the coil of varied fill factor. For fill factors of 0.4-0.9, the power present receiver, this occurs at a distance of 9.6 m, as shown required is about 75 W, or 6-7× the power used by the in Fig. 23. However, significantly longer-range communica- proposed prototype. These estimates are to be taken as lower tions are possible with a more sensitive B-field sensor. For bounds. The comparison does not account for the efficiency example, let us consider the state-of-the-art ELF sensor used of the driver in each case, current crowding (proximity effect) in the well-known AWESOME instrument [17]. This device or the thickness of the insulation in an electrical coil, or torque uses a much larger detector (area = 1.69 m2), resulting in a between elements in a distributed array of permanent / low input-referred noise of ∼40 fT/Hz1 2 at 100 Hz. In this dipoles. case, the expected useful range of the transmitter increases to 1.19 km, as shown in Fig. 23. F. EFFECTS OF NON-RANDOM DATA Transmission of data by FSK modulation is affected by lim- E. ENERGY CONSUMPTION WITH CP-FSK AND CF-FSK ited channel bandwidth. For example, in our case frequency The energy consumption of CP-FSK and CF-FSK transmis- deviations must remain smaller than 20 Hz to avoid 120 Hz sion was compared using the prototype transmitter. Three interference. As a result, it is not possible to transmit long runs of 100 randomly generated symbols were transmitted sequences of multiple bits with the same sign, as may occur with a bit period of 0.5 seconds and M = 15 symbols in non-random data. To illustrate the problem, consider the using both schemes. Each transmission was performed twice. case of the M = 4 level CP-FSK waveform used to transmit Results are tabulated in Table 1. No significant difference data with the prototype transmitter. The signal corresponding

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in the original encoding scheme were assigned to values beginning with +3, and were not changed by the cipher. As a result, the control bits cause a net positive accumula- tion of frequency shift over time which is not removed by the phase reduction cipher. The cipher is seen to be effective at removing some of the non-random shift caused by characters A-Z.

VI. SAMPLE DATA ENCODING Here is presented the same message transmitted in the long-duration message transmission experiments, followed FIGURE 25. Sequence of 5 non-random CP-FSK bits showing required by the steps applied to produce the transmission signal m(t). frequency discontinuities for data transmission. The transmitted message is the following 233 characters with no new-line encoding. WHAT A PIECE OF WORK IS MAN! HOW NOBLE IN REASON, HOW INFINITE IN FACULTY. IN FORM AND MOVING, HOW EXPRESS AND ADMIRABLE. IN ACTION, HOW LIKE AN ANGEL. IN APPREHENSION, HOW LIKE A GOD. THE BEAUTY OF THE WORLD, THE PARAGON OF ANIMALS. The Burrows-Wheeler transform is applied to the data. The first step of this transform is to add beginning and end FIGURE 26. Comparison of accumulated frequency shift for non-random of sequence markers, shown here as ’/’ and ’ŕespectively. data: (a) original data, and (b) with a phase reduction cipher. This increases the length of the output by two for a total of 235 characters to be transmitted. to five transmitted bits from the encoded excerpt of Shake- speare’s Hamlet are shown in Fig. 25. The first bit is a +3, /.ETNDESMNFNEWNNA,,,,!..E. which may only be transmitted as a transition from the lowest EWKWWSDWNYEEAN.,FFENGNNNDS FSK level to the highest level. At the highest level, a smooth ELYD R F RM M PEHE OA transition could be used to transmit 0, −1, −2, or −3, but the EAANNLOAKKHTLCHHLRBIRGHR O next bit in the sequence is also +3. Therefore a discontinuity OO N NN AWTTTE PLLN is required to limit transmit bandwidth, as shown. This behav- VFSTM NRIIERBB AURI D ior is compared to the ideal nature of the transition between IAIIIOIAOOOAAIIAAI ENG G bits 3 and 4 in the sample, which is a smooth transition. The SIIWWFMHHHHH APXIA PPOOOS transition from bit 3 to bit 4 would have lower τmod than the ILNAEAI CULCAOOOOOO\ ETT transition from bit 1 to 2. Compression is applied using run length encoding. To visu- Data transmission would be most power efficient if there alize the effect, the run-counter character is written explic- were no frequency discontinuities such as those shown itly as (xN) where N is the number of times the previous in Fig. 25. This is only feasible for random data. Non-random character is repeated in the uncompressed sequence. Each data will frequently require transmission of multiple repeated counter is expressed as a single special character in the imple- positive or negative values which results in discontinuities mented reduced character set. The result is a sequence of shown in the figure. This problem is visualized by plotting 208 characters. the accumulated frequency shift 1f across the number of transmitted bits in a sample 208-byte sequence of the previ- /.ETNDESMNFNEWN(x2)A,(x4)!.(x2) ously described experiment. Fig. 26(a) shows that the accu- E.EWKW(x2)SDWNYE(x2)AN.,F(x2)EN mulated frequency shift can reach relatively large values. One GN(x3)DSELYD(x2)R F RM M(x5)PEH proposed fix was to employ a substitution cipher before data E OAEA(x2)N(x2)LOAK(x2)HTLCH(x2) encoding from base-36, assigning the most commonly used LRBIRGHR O(x3) N N(x2) AWT(x3) characters to average zero or low shift bytes. For example, E(x5)PL(x2)N(x6)VFSTM NRI(x2)ER assigning the most common letters in the English language, B(x2)(x2)AURI D IAI(x3)OIAO(x3) namely ’e’, ’t’, and ’a’, to transmit bytes (0,0), (+1,−1), A(x2)I(x2)A(x2)I ENG(x3)GSI(x2) and (−1,+1) respectively. The result of applying this cipher W(x2)FMH(x5)(x2)APXIA P(x2)O(x3) is shown in Fig. 26(b). Control and special character bits SILNAEAI(x3)CULCAO(x6)\(x2)ET(x2)

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Finally each character is encoded to two bit bytes using The transmitted message is the following 233 characters with septenary bits. The resulting stream is 208 bytes transmitted no new-line encoding. as 416 bits. WHAT A PIECE OF WORK IS MAN! 1606224535212244343523352252356114 HOW NOBLE IN REASON, 3663460661220622523252614421523554 HOW INFINITE IN FACULTY. 2261143506362361223524356221442233 IN FORM AND MOVING, 5421606143602360433460346064412225 HOW EXPRESS AND ADMIRABLE. 2260401422146135613340143261254533 IN ACTION, HOW LIKE AN ANGEL. 2025613343153043242543604062603560 IN APPREHENSION, HOW LIKE A GOD. 3561601452456222606441336135606551 THE BEAUTY OF THE WORLD, 2344453460354330612243156160611450 THE PARAGON OF ANIMALS. 4330602160301430624030144062146130 The Burrows-Wheeler transform is applied to the data. 6114613060223524606224443061526123 The first step of this transform is to add beginning and end 3425646061144153301460416140624430 of sequence markers, shown here as ’/’ and ’ŕespectively. 3335142214306062205033201440652660 This increases the length of the output by two for a total 61224561 of 235 characters to be transmitted. Using T = 4 s, this sequence takes 1664 seconds or 27 m s /.ETNDESMNFNEWNNA,,,,!..E. 44 s. Implementing 8Y0 (8 data bits, one parity bit, zero stop EWKWWSDWNYEEAN.,FFENGNNNDS bits) would increase the size of transmissions by a factor of 9 , 8 ELYD R F RM M PEHE OA here resulting in 468 bits instead of 416 for a 12.5% increase EAANNLOAKKHTLCHHLRBIRGHR O in transmission time, up to 1872 s (31 m 12 s). OO N NN AWTTTE PLLN VFSTM NRIIERBB AURI D VII. CONCLUSION IAIIIOIAOOOAAIIAAI ENG G We have described the design of miniaturized power-efficient SIIWWFMHHHHH APXIA PPOOOS ELF transmitters based on the mechanical rotation of ILNAEAI CULCAOOOOOO\ ETT permanently-polarized dipoles. The latter can use permanent Compression is applied using run length encoding. To visu- magnets (ferromagnets, suitable for ELF) or electrets (fer- alize the effect, the run-counter character is written explicitly roelectrics, suitable for VLF) [2]. The moment of inertia as (xN) where N is the number of times the previous character of the rotating dipoles must be minimized to reduce peak is repeated in the uncompressed sequence. Each counter is electrical power and increase the data rate. The use of a expressed as a single special character in the implemented distributed array of N > 1 sub-elements minimizes overall reduced character set. The result is a sequence of 208 charac- inertia, while long and thin cylinders are optimal geometries ters. for minimizing the inertia of each sub-element. However, such elongated shapes are difficult to manufacture in practice. /.ETNDESMNFNEWN(x2)A,(x4)!.(x2) The high-speed rotation of the magnetized cylinders is also E.EWKW(x2)SDWNYE(x2)AN.,F(x2)EN accompanied by formidable mechanical design challenges GN(x3)DSELYD(x2)R F RM M(x5)PEH (balancing, dynamic stability, etc.), which will be addressed E OAEA(x2)N(x2)LOAK(x2)HTLCH(x2) in future work. LRBIRGHR O(x3) N N(x2) AWT(x3) An ELF transmitter constructed using a mechanically- E(x5)PL(x2)N(x6)VFSTM NRI(x2)ER rotating magnetic dipole was evaluated to demonstrate its use B(x2)(x2)AURI D IAI(x3)OIAO(x3) for non-line-of-sight wireless communications in conductive A(x2)I(x2)A(x2)I ENG(x3)GSI(x2) media. Data was successfully transmitted through walls and W(x2)FMH(x5)(x2)APXIA P(x2)O(x3) floors, in particular from inside a laboratory to a hallway SILNAEAI(x3)CULCAO(x6)\(x2)ET(x2) on a different floor of the building. Design challenges were Finally each character is encoded to two bit bytes using considered for the receiver, including the impact of power line septenary bits. The resulting stream is 208 bytes transmitted interference on the effectiveness of long-range data transmis- as 416 bits. sion. Future work will focus on improved receiver designs to maximize the useful transmission range. 1606224535212244343523352252356114 3663460661220622523252614421523554 APPENDIX 2261143506362361223524356221442233 SAMPLE DATA ENCODING 5421606143602360433460346064412225 Here is presented the same message transmitted in the 2260401422146135613340143261254533 long-duration message transmission experiments, followed 2025613343153043242543604062603560 by the steps applied to produce the transmission signal m(t). 3561601452456222606441336135606551

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2344453460354330612243156160611450 [21] DARPA. A Mechanical Based Antenna (AMEBA). 4330602160301430624030144062146130 Accessed: Dec. 19, 2016. [Online]. Available: https://govtribe.com/ opportunity/federal-contract-opportunity/a-mechanical-based-antenna- 6114613060223524606224443061526123 ameba-hr001117s0007 3425646061144153301460416140624430 [22] S. Gong, Y. Liu, and Y. Liu, ‘‘A rotating-magnet based mechanical antenna 3335142214306062205033201440652660 (RMBMA) for ELF-ULF wireless communication,’’ Prog. Electromagn. Res. M, vol. 72, pp. 125–133, Aug. 2018. 61224561 [23] H. C. Burch, A. Garraud, M. F. Mitchell, R. C. Moore, and D. P. Arnold, ‘‘Experimental generation of ELF radio signals using a rotating magnet,’’ Using Ts = 4 s, this sequence takes 1664 seconds or 27 m IEEE Trans. Antennas Propag., vol. 66, no. 11, pp. 6265–6272, Nov. 2018. 44 s. Implementing 8Y0 (8 data bits, one parity bit, zero stop [24] M. A. Kemp, M. Franzi, A. Haase, E. Jongewaard, M. T. Whittaker, bits) would increase the size of transmissions by a factor of 9 , M. Kirkpatrick, and R. Sparr, ‘‘A high Q piezoelectric resonator as 8 a portable VLF transmitter,’’ Nature Commun., vol. 10, Apr. 2019, here resulting in 468 bits instead of 416 for a 12.5% increase Art. no. 1715. in transmission time, up to 1872 s (31 m 12 s). [25] J. Xu, C. M. Leung, X. Zhuang, J. Li, S. Bhardwaj, J. Volakis, and D. Viehland, ‘‘A low frequency mechanical transmitter based on magne- toelectric heterostructures operated at their resonance frequency,’’ MDPI REFERENCES Sensors, vol. 19, no. 4, p. 853, Feb. 2019. [1] M. T. B. Tarek, S. Dharmasena, A. Madanayake, S. Choi, J. Glickstein, [26] C. Zwyssig, S. D. Round, and J. W. Kolar, ‘‘Analytical and experimental J. Liang, and S. Mandal, ‘‘Power-efficient data modulation for all- investigation of a low torque, ultra-high speed drive system,’’ in Proc. IEEE mechanical ULF/VLF transmitters,’’ in Proc. IEEE 61st Int. Midwest Ind. Appl. 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Hürlimann, M. Poitzsch, and Y.-Q. Song, ‘‘An ultra-broadband low-frequency magnetic resonance system,’’ J. Magn. Reson., vol. 242, pp. 113–125, May 2014. [15] A. J. Smith, ‘‘VELOX: A new VLF/ELF receiver in Antarctica for the global geospace science mission,’’ J. Atmos. Terr. Phys., vol. 57, no. 5, pp. 507–524, 1995. [16] S. K. Harriman, E. W. Paschal, and U. S. Inan, ‘‘Magnetic sensor design JARRED S. GLICKSTEIN (S’16) received the B.S. for femtotesla low-frequency signals,’’ IEEE Trans. Geosci. Remote Sens., and M.S. degrees in electrical engineering from vol. 48, no. 1, pp. 396–402, Jan. 2010. Case Western Reserve University, Cleveland, OH, [17] M. B. Cohen, U. S. Inan, and E. W. Paschal, ‘‘Sensitive broadband USA, in 2016 and 2018, respectively, where he is ELF/VLF radio reception with the AWESOME instrument,’’ IEEE Trans. currently pursuing the Ph.D. degree in electrical Geosci. Remote Sens., vol. 48, no. 1, pp. 3–17, Jan. 2010. engineering. [18] X. Xu and Y. E. Wang, ‘‘Beyond the efficiency bandwidth limit with switched electrically small antennas,’’ in Proc. IEEE Antennas Propag. He was a Research Assistant with the Center Soc. Int. Symp., Jun. 2007, pp. 2261–2264. for Global Health and Diseases, Case Western [19] U. Azad and Y.E. Wang, ‘‘Direct antenna modulation (DAM) for enhanced Reserve University, in 2015, where he has been capacity performance of near-field communication (NFC) link,’’ IEEE a Research Assistant with the Integrated Circuits Trans. Circuits Syst. I, Reg. Papers, vol. 61, no. 3, pp. 902–910, Mar. 2014. and Sensor Physics Lab, since 2015. His research interests include analog [20] V. J. Phillips, ‘‘The Alexanderson alternator,’’ Eng. Sci. Educ. J., vol. 6, sensors and instrumentation design, electromechanical devices, experiment no. 1, pp. 37–42, Feb. 1997. automation, and novel applications in magnetic materials.

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JIFU LIANG (M’16) received the B.E. degree in ARJUNA MADANAYAKE (SM’08) received the optoelectronic information engineering from the B.Sc. degree (Hons.) in electronic and telecom- Huazhong University of Science and Technology, munication engineering from the University of Wuhan, China, in 2014, and the M.S. degree in Moratuwa, Moratuwa, Sri Lanka, in 2002, and the electrical engineering from Case Western Reserve M.Sc. and Ph.D. degrees in electrical engineer- University, Cleveland, OH, USA, in 2016, where ing from the University of Calgary, Calgary, AB, he is currently pursuing the Ph.D. degree in elec- Canada, in 2004 and 2008, respectively. trical engineering. He is currently an Associate Professor with the He is currently a Research Assistant with Department of Electrical and Computer Engineer- the Integrated Circuits and Sensor Physics Lab, ing, Florida International University, Miami, FL, Case Western Reserve University. His research interests include integrated USA. His research interests include multidimensional signal processing, circuits for biomedical and array processing applications. analog/digital and mixed-signal electronics, and VLSI for fast algorithms.

SOUMYAJIT MANDAL (S’01–M’09–SM’14) SEUNGDEOG CHOI (S’07–M’12–SM’16) rec- received the B.Tech. degree in electronics and eived the B.S. degree in electrical and computer electrical communications engineering from IIT engineering from Chung-Ang University, in 2004, Kharagpur, India, in 2002, and the M.S. and Ph.D. the M.S. degree from Seoul National University, degrees in electrical engineering from the Mas- South Korea, in 2006, and the Ph.D. degree in sachusetts Institute of Technology (MIT), Cam- electric power and power electronics from Texas bridge, MA, USA, in 2004 and 2009, respectively. A&M University, College Station, in 2010. He was a Research Scientist with Schlumberger- He was with LG Electronics, Seoul, South Doll Research, Cambridge, MA, USA, from Korea, from 2006 to 2007, and a Research Engi- 2010 to 2014. He is currently an Assistant Pro- neer with Toshiba International Corp., Houston, fessor with the Department of Electrical Engineering and Computer Science, TX, USA, from 2009 to 2012. He was an Assistant Professor with The Case Western Reserve University, Cleveland, OH, USA. He has over 60 pub- University of Akron, from 2012 to 2018. He has been an Associate Professor lications in peer-reviewed journals and premier conferences. His research with Mississippi State University, Starkville, since 2018. He has coauthored interests include analog and biological computation, magnetic resonance a book. He has published more than 100 articles including journal arti- sensors, low-power analog and RF circuits, and precision instrumentation cles (published/under review). He has published more than 100 articles in for various biomedical and sensor interface applications. He was a recipient around 90 peer-reviewed IEEE conferences. He holds around 20 patents of the President of India Gold Medal, in 2002, delivered the Annual MIT (registered/pending). His research interests include degradation modeling, Microsystems Technology Laboratories Doctoral Dissertation Seminar in fault tolerant control, and the fault tolerant design of electric machines, recognition of outstanding research of interest to a broad audience, in 2009, power electronics, battery, solar panel, and wider vehicular/aircraft microgrid and the T. Keith Glennan Fellowship, in 2016. systems.

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